BOOK I.

SPHERICAL PROBLEMS,

125

OBD, equal the sum of the interior anglesof the polygon EFGHI: Whence, the areasof the two figures are equal. (C. II. P. I.)

Also, since the angles at O, are all rightangles, and the side BD=DC=AC=ABjthe figure AB D C is a square.

PROBLEM VI.

With. two given angles A, B, to makea spherical parallelogram, having one ofits sides equal to a given arch CD, ofa given circle. — (PI. 6. fig, 8.)

ANALYSIS, Suppose the thing done, andthat E F C D is the required parallelogram,having the given side C D, and the angleFCD = A, and angle CDE = B.

Produce F C and D E, both ways to meetin V and I: Then, because, angles F C D,E D C are given; D CI is also given as wellas CDI; and, hence, the following

CON. Upon CD, lay off the angles DCI,CDI, and produce CI and D I, till theytneet in I and V. From V, lay off VF — D I,And V E = C I. Lastly, join F, E, with A